The logistic map constitutes one of the most well-known maps in science. It has peculiar characteristics, it is able to generate topological chaos and ergodic chaos, and it reveals various routes to chaos. The transition to chaos is made by way of the period-doubling bifurcations, the type-I intermittency appears, too. The logistic map is a perfect generalization of numerous classical economic models covering economic growth, monopoly rules, inflation, or the theory of consumer choice. Consequently, it can be regarded as a kind of a portal through which the chaos and complexity theories have been introduced to economics. This eventually leads to the creation of a new trend – the complexity economics which has been successfully competing with the mainstream economics.